vector bundle

vector bundle

English

Noun

vector bundle (plural vector bundles)

1. (topology, category theory) A fiber bundle for which the fiber is a vector space.
   • 1995, Mauro Beltrametti, Andrew John Sommese, The Adjunction Theory of Complex Projective Varieties, Walter de Gruyter, page 8,

     Let E and F be two vector bundles on a compact algebraic set X.

   • 2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5,

     This^[sic] solutions actually depend on the choice of a trivialisation ${\\displaystyle \\xi }$ of the universal family ${\\displaystyle {\\mathcal {P}}(n,d)}$ of stable vector bundles of rank ${\\displaystyle n}$ and degree ${\\displaystyle d}$.

   • 2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130,

     Definition 6.1.5 A non-zero vector bundle ${\\displaystyle {\\mathcal {F}}}$ on ${\\displaystyle X}$ is said to be decomposable if it can be written as ${\\displaystyle {\\mathcal {F}}_{1}\\oplus {\\mathcal {F}}_{2}}$ with ${\\displaystyle {\\mathcal {F}}_{1}}$ and ${\\displaystyle {\\mathcal {F}}_{2}}$ non-zero vector bundles. Otherwise it is said to be indecomposable.

Hypernyms

• fiber bundle

Hyponyms

• tangent bundle

Meronyms

• zero section

Translations

Translations

Finnish: vektorikimppu German: Vektorbündel n

Further reading

• Fiber bundle on Wikipedia.Wikipedia
• Coherent sheaf on Wikipedia.Wikipedia
• Holomorphic vector bundle on Wikipedia.Wikipedia
• vector bundle on nLab
• Vector Bundle on Wolfram MathWorld
• Vector bundle on Encylopedia of Mathematics
• Vector bundle, algebraic on Encylopedia of Mathematics
• Vector bundle, analytic on Encylopedia of Mathematics